So he/she's given you notice. When was it given to you? Is it normal notice, or have they issued a S21?
In your shoes, I would:
Tell the landlord that you are willing to help them out, if they are willing to return the favour. If they accept less than 1 months notice when you find a property, then you will continue to accept viewings for certain periods a week, and would be willing to leave for the duration and keep it at a tidy standard.
If they are not willing to do so, then unfortunately your goodwill has run out, and you will be unable to accept viewings at all while still a tenant of the property, as you are entitled to 'quiet enjoyment' of your home.
With regards to the notice period- if he gave it before June 1st, he needed to give you 6 months notice because of covid, regardless of what the contract says.
If he gave you it after June 1st, he needs to give you 4 months notice, regardless of what your contract says.
Those dates are also just a starting point. When your notice period ends, he then needs to issue a S21, which means he can then take you to court to evict you. The list for this is currently months/years long.
So, if he really wants to be unreasonable with you, you can make it clear that you won't be leaving until you have found somewhere that accepts his month notice period, regardless if thats the end of August or not, and unfortunately you still won't be taking viewings while in the property, as is your right. He could have hold of that house for a very long time if you don't want to play ball.